If your tofu block is thick, slice in half horizontally so the piece of tofu is about ¾ to 1 inch thick (2-2.5cm). Place in a shallow plate that will fit inside your steamer. Sprinkle ⅛ teaspoon salt and drizzle ⅛ teaspoon sesame oil on top.
Bring a pot with plenty of water to a boil and then blanch broccoli florets for 1-2 minutes. Remove when broccoli is still very crisp-tender. You can also give it a very quick rinse under cold water to stop the cooking. Set aside to let it drain.
While doing Step 1 and 2, place a pan over medium-high heat. Once it is hot, add cooking oil to lightly coat the bottom. Then add mushrooms and sear until both sides are browned, about a couple minutes each side. Transfer to a plate.
Adjust the heat to medium and add a little more oil to the pan. Add onion and sauté until fragrant, about 30 seconds. Then add carrots and cook for 30-45 seconds. Add minced garlic and cook briefly until garlic is fragrant.
Add seared mushrooms back to the pan and give everything a stir. Then add stock and let it come to a rapid simmer. Add oyster sauce, soy sauce and stir well.
Dissolve cornstarch in water, and slowly pour the cornstarch slurry into the sauce while stirring to thicken it to your liking. Then add blanched broccoli to the pan and toss to coat everything with the sauce. You can add ⅛ teaspoon of sesame oil to the sauce for more fragrance. Also adjust seasonings to taste. Turn off the heat.
When you start Step 4, also place the plate with the tofu in your steamed and steam until heated through, about 6-7 minutes. When the tofu is done steaming, pour off the liquid that has pooled at the bottom of the plate.
Pour the mushroom and vegetables stir-fry mixture over the steamed tofu. Sprinkle some pepper on top and serve hot immediately.